In modeling this timeseries, we could assume that the number of lynx
trapped in a given year is falls into one of \(k\) states, which are
normally distributed with some unknown mean \(\mu_i\) and variance
\(\sigma^2_i\) for each state

To learn the latent variables, \(\mu_i\)\(\sigma^2_i\), we
would use a normal inverse-chi-square likelihood

The normal inverse-chi-square likelihood is the conjugate univariate
normal likelihood in data microscopes. We also have normal likelihood,
the normal inverse-wishart likelihood, optimized for multivariate
datasets.

It is important to model univariate normal data with this likelihood as
it acheives superior performance on univariate data.

In both these examples, we found variables that were amenable to being
modeled as univariate normal:

Univariate datasets

Datasets containing real valued variables with near zero correlation

To import our univariate normal inverse-chi-squared likelihood, call:

frommicroscopes.modelsimportnichasnormal_inverse_chisquared

Datamicroscopes is developed by Qadium, with funding from the DARPAXDATA program. Copyright Qadium 2015.